Solve a, b, c, d please and thank you. It’ll help a lot.

By using sample standard deviation - (1) N or n = 20

(2) X or μ = 43.4

(3) σ = 9.78 and s = 10.04

Why does sample standard deviation exist?

When we talk about a sample standard deviation, we're not talking about population standard deviation. The average amount by which a group of values deviates from their mean is shown by the statistical measure of variability known as the standard deviation.

We are given with the following data set below;

{51, 48, 42, 43, 48, 48, 46, 15, 29, 45, 47, 55, 46, 35, 47, 48, 54, 26, 53, 42}

(1) As we can see in the above data that there are 20 data values in our data set which means that the value of N or n (numner of observations) is 20.

(2) The formula for calculating Mean of the data, i.e. X or μ is given by;

       Mean  =  51 +48+ 42+ 43+ 48 + 48 + 46+ 15+ 29+ 45+ 47+ 55+ 46+ 35+ 47+ 48+ 54+ 26+ 53+ 42/20

                = 868/20 = 43.4

So, the value of  X or μ   is 43.4.

(3) The formula for calculating population standard deviation () is given by;

  Standard deviation, σ  = √(51 - 43.4)² + (48 - 43.4)² + .........+(42 - 43.4)²/20

        =  9.78

Similarly, the formula for calculating sample standard deviation (s) is given by;

       Sample Standard deviation, s =  

                       √(51 - 43.4)² + (48 - 43.4)² + .........+(42 - 43.4)²/20 - 1

                      =  10.04

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Answer:

Therefore, there are 20 girls in the class of fifth-graders.

In mathematics, a fraction represents a part of a whole or a division of two numbers. It is written in the form of a numerator and a denominator separated by a horizontal bar (also known as a fraction bar). The numerator represents the number of equal parts being considered, while the denominator represents the total number of equal parts in the whole or the divisor of the division.

Here,

Let the number of girls in the class be represented by 'g'.

According to the problem, the number of boys is 3/4 as many as the number of girls. This means:

Number of boys = (3/4) * number of girls

Number of boys = (3/4) * g

The total number of students in the class is given as 35. So we have:

Number of girls + Number of boys = Total number of students

g + (3/4)g = 35

Simplifying the equation, we get:

(7/4)g = 35

Dividing both sides by 7/4, we get:

g = 20

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Answer:

Step-by-step explanation:1.4 -1, 1 2, -1

Answer: We can first find the dot product of vec r with hat j and hat k:

vec r * hat j = (3 hat i - 2 hat j + 6 hat k) * (- hat j) = -2

vec r * hat k = (3 hat i - 2 hat j + 6 hat k) * hat k = 6

Substituting these values into the expression given, we get:

(vec r * hat j).(vec r * hat k) - 12 = (-2) * (6) - 12 = -24

Therefore, the value of (vec r * hat j).(vec r * hat k) - 12 is -24.

Step-by-step explanation:

Answer:

$4.50

Step-by-step explanation:

There are 12 inches in a foot. 18 inches is 1.5 feet.

1 foot of wire is $3.00 and a half of foot should be $1.50.

1.5 feet of wire should cost $4.50

1.5 ft × $3/ft

= $4.50

Where F_pivot is the magnitude of the force exerted on the pivot point.

What are perpendicular lines?

Perpendicular lines are lines that intersect at a right angle (90 degrees). In other words, if you draw a line perpendicular to another line, the two lines will form four right angles at the point where they intersect.

(a) The torque applied by the adult rider (on the left) can be calculated as the product of the force applied by the rider and the perpendicular distance from the pivot to the force. Let F_a be the force applied by the adult rider and let r_a be the perpendicular distance from the pivot to the force. Then, the torque applied by the adult rider is:

τ_a = F_a * r_a

The perpendicular distance r_a can be calculated using the Pythagorean theorem:

r_a = sqrt((L/2 - d)^2 + Xoffset^2)

Therefore, the torque applied by the adult rider is:

τ_a = F_a * sqrt((L/2 - d)^2 + Xoffset^2)

(b) Similarly, the torque applied by the child rider (on the right) can be calculated as:

τ_c = F_c * sqrt((L/2 + d)^2 + Xoffset^2)

where F_c is the force applied by the child rider and r_c is the perpendicular distance from the pivot to the force, which can be calculated using the Pythagorean theorem.

(c) The torque applied by the board can be calculated as the sum of the torques applied by the two riders:

τ_b = τ_a + τ_c

Substituting the expressions for τ_a and τ_c, we get:

τ_b = F_a * sqrt((L/2 - d)^2 + Xoffset^2) + F_c * sqrt((L/2 + d)^2 + Xoffset^2)

(d) To determine the distance d in terms of given quantities and variables, we can use the condition for static equilibrium, which requires that the sum of the torques about the pivot point is zero:

τ_a + τ_c = 0

Substituting the expressions for τ_a and τ_c and simplifying, we get:

F_a * (L/2 - d) = F_c * (L/2 + d)

Solving for d, we get:

d = (F_a/F_c - 1) * L/4

Substituting F_a = Mg and F_c = mg, where M is the mass of the adult rider, m is the mass of the child rider, and g is the acceleration due to gravity, we get:

d = (M/m - 1) * L/4

(e) The magnitude of the force exerted on the pivot point by the see-saw while in use can be calculated using the condition for static equilibrium, which requires that the sum of the forces in the vertical direction is zero:

F_a + F_c = Mg + mg

Substituting F_a = Mg and F_c = mg, we get:

F_pivot = Mg + mg

Therefore, where F_pivot is the magnitude of the force exerted on the pivot point.

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Answer: There is a 5.32544378% Chance of a face card being pulled twice

Step-by-step explanation: If there is 52 cards in a deck, and 12 of them are face cards, there is roughly a 23% (23.0769%) chance of pulling one in the first draw. Multiply .230769 x .230769 and you get .0532544378 which equals 5.32544378%

The value of the expression 2.1 × 1.6 = 3.36.

Decimals are a collection of numbers falling between integers on a number line. They are only an additional mathematical representation of fractions. Decimals allow us to express quantifiable quantities like length, weight, distance, money, etc. with more accuracy. Integers, also known as whole numbers, are represented to the left of the decimal point, while decimal fractions are shown to the right of the decimal point.

Given that the expression is: 2.1 × 1.6.

2.1 × 1.6 can be written as:

2.1 × 1.6 = 21/10 × 16/10

Multiply the numerator and denominator:

21/10 × 16/10 = 336/100

Covert the fraction into decimal:

336/100 = 3.36

Hence, the value of the expression 2.1 × 1.6 = 3.36.

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Answer:

50

Step-by-step explanation:

A Venn diagram is very helpful for this picture and I've included one in the attached.

If we look at the numbers we're given, we see that the numbers do not add up to 500 as 350 + 300 + 200 = 850.

However, we can work through the numbers to find the exact values and eventually the number of people that liked neither rock nor country.

Since 200 people like both rock and country, these people are part of the 350 people that like rock.

We can find the number of people who like rock only by subtracting 200 from 350:

350 - 200 = 150 (Rock only)

Using the same logic from above, we know that the 200 people who like both rock and country are a part of the 300 people who like country.

We can find the number of people who like country only by subtracting 200 from 300:

300 - 200 = 100 (Country only)

Currently, we have 450/500 as 150 + 200 + 100 = 450.

Now, we can find the number of people who like neither rock nor country by subtracting 450 from 500:

500 - 450 = 50 (Neither rock nor country)

We can check that the numbers we found equal 500:

Rock only + Both rock and country + Country only + Neither rock nor country = Total amount of music lovers surveyed

150 + 200 + 100 + 50 = 500

500 = 500

(**In the attached Venn diagram, M stands for the total set of music lovers, R stands for rock only, B stands for both, C stands for country only, and N stands for neither)

Answer:

[tex](x-4)^2+(y+1)^2=162[/tex]

Step-by-step explanation:

Determine r² by using the equation of a circle and plugging in the center (h,k)->(4,-1) as well as (x,y)->(13,8):

[tex](x-h)^2+(y-k)^2=r^2\\(x-4)^2+(y-(-1))^2=r^2\\(13-4)^2+(8+1)^2=r^2\\9^2+9^2=r^2\\81+81=r^2\\162=r^2\\[/tex]

Hence, the equation of the circle that meets these criteria is[tex](x-4)^2+(y+1)^2=162[/tex]

The solution of the graphs are as follows

first graph

second graph

The graphs consist of two sets of equations plotted, each has shade peculiar to the equation.

The solution of the graph consist of the ordered pair that fall within the parts covered by the two shades

For the first graph by the left, the solutions are

For the second graph by the left, the solutions are

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Step-by-step explanation:

For RIGHT triangles  :  sin ( angle) = opposite LEG / Hypotenuse

   so   sin B = 32 / 68 =  8 / 17

Answer:

9 x 3/9

27/9

27 ÷ 9

Step-by-step explanation:

You're welcome.

Answer:

m = 6

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points on the table (4,6) (5,12)

We see the y increase by 6 and the x increase by 1, so the slope is

m = 6

So, the slope is 6

The interest earned on GH 2500 at 5% p.a. for 4 years is GH 500.
The principal that gains an interest of GH 2590 in 5 years at 7% per annum is approximately GH 7400.

What is simple interest ?

Simple interest is a type of interest that is calculated on the principal amount of a loan or investment at a fixed rate for a specified period of time. It is based only on the principal amount, and does not take into account any interest earned on previous periods.

The formula for simple interest is:

I = P * R * T

where:

According to the question:
a) Using the simple interest formula, we have:

I = (P * R * T) / 100

Substituting P = GH 2500, R = 5%, and T = 4 years, we get:

I = (2500 * 5 * 4) / 100 = 500

Therefore, the interest earned on GH 2500 at 5% p.a. for 4 years is GH 500.

b) Using the same formula, we can solve for the principal P:

I = (P * R * T) / 100

2590 = (P * 7 * 5) / 100

2590 = (35P) / 100

35P = 2590 * 100

P = (2590 * 100) / 35

P ≈ GH 7400

Therefore, the principal that gains an interest of GH 2590 in 5 years at 7% per annum is approximately GH 7400.

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Sea "x" la longitud de cada lado del jardín original en metros.

La superficie del jardín original es x^2 m².

Si cada lado del jardín original se aumenta en 5 m, el nuevo lado del jardín será de (x+5) metros, y la nueva superficie será (x+5)^2 m².

Según el problema, la nueva superficie total es de 121 m²:

(x+5)^2 = 121

Tomando la raíz cuadrada en ambos lados:

x+5 = 11

Restando 5 en ambos lados:

x = 6

Por lo tanto, la longitud de cada lado del jardín original es de 6 metros.

Por lo tanto, la respuesta correcta es O 6 metros.

x - the length of each side of the original garden

A = x²

( x + 5 )² = 121  /√

x + 5 = 11,  or  x + 5 = - 11;

x = 11 - 5

x = 6  ( another solution in negative )

Answer:

A ) 6 m

The values of the function from the graph are h(7) = 10, h(0) = 9, h(t) = 8, t = 5 and  h(t) = 0, t = 4

Given that the graph is the graph of height as a function of time

To calculate the values of h(t) from the graph of g(x), we need to follow these steps

Using the above, we have the following

h(7) = 10

h(0) = 9

h(t) = 8, t = 5

h(t) = 0, t = 4

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Answer:16

Step-by-step explanation:

average is similar to mean

you get the Total value and divide it with the number of values added

Answer:

57

Step-by-step explanation:

Okay, So we have this person That has 81% average before the quiz. For a course That score includes everything, but the final, which counts for 25% of the course grade, was the best course grade you your friend can earn. Okay, The best course grade given to me makes me. Mhm. 100. So we have .81 times. Actually we'll keep this as 81, times .75 right Plus 100 times. Excuse ME, Time 0.25. This is equivalent to 81 times 0.75. Mhm. This is equivalent to 81 times .75 plus 100 times 0.25, Which equals 85.75%. Now that's for part one. Report to we have what is the minimum score? Turn to 75%. So we have 75 equal to 81 times 0.75 Plus X. Times zero 25. So 81 times 0.75 equals 60.75 75- is value mhm. Is equal to 14.25. So we have 0.25 x. And if we divide 14.25 over 0.25, we isolate X. So the minimum score to get a 75 is a 57

Answer:

The farmer uses 221 pipes in total: 124 plastic pipes and 97 metal pipes.

Answer:

To find out how many pipes the farmer used in total, we simply add the number of plastic pipes to the number of metal pipes:

Total pipes = Plastic pipes + Metal pipes

Total pipes = 124 + 97

Total pipes = 221

Therefore, the farmer used a total of 221 pipes for the irrigation system.

Answer:

shelf area = 19018.33 square inches

Step-by-step explanation:

shelf area calculation:

Ignacio makes a display shelf from 4 wooden boards. All angles formed by the boards are right angles. Ignacio plans to stain all faces of the shelf, except the back face, which will be against the wall. What is the total area Ignacio will stain? Show your work. 512 7 in. 1 2 32 in. 30 in. 72 17 56 9 in. 4 in. 512 24 A 329-30.7 72

To find the total area that Ignacio will stain, we first need to determine the area of each face that will be stained.

Let's label the boards as follows:

Board 1: 512 in x 7 in

Board 2: 12 in x 32 in

Board 3: 30 in x 72 in

Board 4: 17 56/9 in x 4 in

For each board, we need to find the total area of all the faces that will be stained.

Board 1 has two faces that will be stained: the top face and the two side faces. The area of the top face is 512 in x 7 in = 3584 in^2. The area of each side face is 512 in x 12 in = 6144 in^2. So the total area of all three faces is 3584 in^2 + 2 x 6144 in^2 = 15872 in^2.

Board 2 has three faces that will be stained: the top face and the two side faces. The area of the top face is 12 in x 32 in = 384 in^2. The area of each side face is 12 in x 4 in = 48 in^2. So the total area of all three faces is 384 in^2 + 2 x 48 in^2 = 480 in^2.

Board 3 has three faces that will be stained: the top face and the two side faces. The area of the top face is 30 in x 72 in = 2160 in^2. The area of each side face is 72 in x 4 in = 288 in^2. So the total area of all three faces is 2160 in^2 + 2 x 288 in^2 = 2736 in^2.

Board 4 has two faces that will be stained: the top face and the side face. The area of the top face is 17 56/9 in x 4 in = 71 2/3 in^2. The area of the side face is 17 56/9 in x 9 in = 158 2/3 in^2. So the total area of both faces is 71 2/3 in^2 + 158 2/3 in^2 = 230 1/3 in^2.

To find the total area that Ignacio will stain, we just need to add up the areas of all the faces that will be stained:

15872 in^2 + 480 in^2 + 2736 in^2 + 230 1/3 in^2 = 19018 1/3 in^2

Therefore, the total area that Ignacio will stain is approximately 19018.33 square inches.

original question :

Ignacio makes a display shelf from 4 wooden boards. All angles formed by the boards are right angles. Ignacio plans to stain all faces of the shelf, except the back face, which will be against the wall. What is the total area Ignacio will stain? Show your work. 512 7 in. 1 2 32 in. 30 in. 72 17 56 9 in. 4 in. 512 24 A 329-30.7 72

chatgpt

In a diagram,

Then,

[tex]\dfrac{DE}{BC}=n[/tex]

For example, suppose that n=2; thus,

[tex]DE=2BC\longrightarrow2\times CA[/tex]

We can form a new triangle DEF whose side EF is parallel to CA; therefore,

[tex]\longrightarrow EF=2CA[/tex]

a) The expression for the stable fixed point is P* = (1 + sqrt(1 - 4h)) / 2

b) There exists a fixed point for all values of h less than or equal to 1/4.

The fixed points of the model are the values of P at which dP/dt = 0. Therefore, we need to solve the equation

P(1-P) - h = 0

Expanding the left-hand side, we get

P - P^2 - h = 0

Rearranging, we get a quadratic equation

P^2 - P + h = 0

Using the quadratic formula, the two solutions for P are

P = (1 ± sqrt(1 - 4h)) / 2

a) The larger root is the stable fixed point, as it corresponds to a minimum of the fish population growth function. Therefore, the expression for the stable fixed point is

P* = (1 + sqrt(1 - 4h)) / 2

b) For the model to have a fixed point, the quadratic equation must have real roots. This occurs when the discriminant (the expression inside the square root) is non-negative

1 - 4h ≥ 0

Solving for h, we get

h ≤ 1/4

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The given question is incomplete, the complete question is:

This problem explores some questions regarding the fishery model

dP/dt =P(1−P)−h

If you have not yet run the Jupyter notebook please do so now. Find analytical expressions for the two fixed points of the model, in terms of h

a) Give an expression for the stable fixed point. You may assume that the larger fixed point is the stable one. b) For what values of h does there exist a fixed point?

The temperature changed by 41°F during the overnight hours, decreasing from 28°F to -13°F.

The difference in temperature from 28°F to -13°F can be shown in one of two ways:

To calculate the change in temperature, the first exponent equation subtracts the initial temperature from the end temperature. The change in this instance is negative and points to a drop in temperature.

The absolute value function is employed in the second statement to guarantee a positive result regardless of whether the temperature rose or fell. The result is the same as the first expression in this instance, but with a positive sign.

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If we solve this inequality for x, we get x 20, which indicates the school equation bake sale must sell at least 20 cakes in order to meet their $200 objective.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

10x ≥ 200 accurately portrays the scenario.

To explain why, consider the following:

Because each cake costs $10, the total amount earned from selling x cakes is 10x.

The aim is to raise at least $200, thus the total amount must be larger than or equal to $200.

As a result, we may describe the circumstance by writing the inequality 10x 200.

If we solve this inequality for x, we get x 20, which indicates the school bake sale must sell at least 20 cakes in order to meet their $200 objective.

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Answer:

A right angled triangle is similar to triangle ABC

Step-by-step explanation:

If you tilt the triangle and put it straight, you'll see that angle C is equal to 90°

And if a triangle has one angle of 90° then it is a right angled triangle

Hope you understand :)

Answer:

Step-by-step explanation:

long leg = 78  (means that 26√3*√3 = 26√9 = 26*3 = 78

for x: Short leg= 26√3

Hypotenuse= 2*26√3 = 52√3 for y

The margin of error in a confidence interval for the population mean includes the standard error of the sample mean and the z or t value associated with a certain level of confidence, usually 95% or 99%. Therefore, the correct answer is (C).

Sampling bias and nonresponse bias are potential sources of error in survey or study design and data collection, but they are not directly related to the construction of a confidence interval.

The desired level of confidence is a key input for determining the z or t value used in the calculation of the margin of error, but it is not included in the margin of error itself. The correct answer is  z or t value associated with a 95% confidence level.

So, the correct option is (C).

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Answer:

Step-by-step explanation:

The inequality in the first equation is x > 8.

The inequality for the second graph is x ≤ -4 since it's a dot.